Dark energy from various approaches

Archan S. Majumdar

S. N. Bose National Centre for Basic Sciences

BSM, Quy nhon, vietnam

Motivations

• Observational evidence for dark energy (present acceleration – supernovae); (weak lensing surveys); (CMB spectrum)

• Origin of dark energy: various candidates or mechanisms: cosmological constant (theoretical difficulties); dynamical dark energy models (scalar fields motivated from unification scenarios); modified gravitational dynamics [f(R), MOND, braneworld, etc..]; numerous other scenarios…

• Three categories discussed here: (i) scalar field dynamics (unification of DE & DM) (ii) back reaction from inhomogeneties (iii) quantum entanglement and dark energy

Dark energy through scalar field dynamics

Quintessence -- potential energy driven acceleration [ASM, Phys. Rev. D 64, 083503 (2001) ]

K-essence – kinetic energy driven acceleration [N. Bose and ASM, Phys. Rev. D 79, 103517 (2009); Phys. Rev. D 80, 103508 (2009)]

2)( V )(2 Vp 0)exp(~ ata

01)()()( 22 aFVFL

Quintessence & k- essence: Perspective

• Inflationary models (kinetic– or potential energy driven) originally motivated from string theoretic (Born-Infeld), braneworld actions. [c.f. Armendariz-Picon, Damour, Mukhanov, (1999) ]

• Subsequently, models for late time acceleration of the universe driven by scalar field kinetic / potential energy. [c.f. Chiba et. al (1999), Steinhardt et. al. (2001), Chimento (2004)….]

• Search for a single field (or similar mechanism) to generate the early and present era acceleration of the universe. [c.f. quintessential inflation: Peebles (1999), Copeland (2000), Majumdar (2001), Sahni (2004)…… ]

• Nature of both dark matter and dark energy are unknown. Could these be manifestations of the same entity ? [c.f. unified models: …...Liddle et. al. (2008)]

Dark energy in the brane-world scenario (ASM, PRD 2001)

Early era inflation and late-time acceleration through same scalar field

Observational data: (a) Inflationary era (CMBR observations, i.e., COBE) (b) Intermediate era (e.g., nucleosynthesis ) (c) Present era (Red-shift (supernovae) , dark matter (lensing)

Constraints on potential parameters

(Scalar field potential not directly measurable) Constraints translate into restrictions on observable parameters such as .....,,, 000 TzwqH

K-essence Model-I (N. Bose and ASM, PRD 2009 )

• Inflationary era: (V ~ constant, or varies slowly)

Field equation:

Energy conservation:

Fixed points of the eq. ( ) correspond to extrema of F.

is an attractor leading to exponential inflation.

• Exit from the inflationary era: slowly moves away from Inflation ends when

MmxLmKxxF plpl42)( )()( VxFL ceV /1)(

06)2( xHFxFxF xxxx 3/ akFx x

VxFHpH x6)(3

p

2

24

0 4,0

K

Lmxx pl

x 0x

10

x

x

Post-inflationary evolution• Stage of kinetic domination after inflation F.E.:

recovering back effectively, kinetic k-essence.

• Energy density:

• Eq. of state:

post-inflation (before radiation domination):

matter domination:

• late time evolution ( ):

03)2( xxxx FHFxF

62

2

3 4 BaA

k

Aa

kC

CxABxF 2)21()(

3242

16

1

a

kAB

BAx

62

2

3

62

2

4

4

BaAk

Aak

C

CBaA

k

w

1w

0w

a 1w

Constraints on model parameters

Observational requirements:• Inflationary era: amplitude of density perturbations ; e-foldings

• Intermediate era: crossover from kinetic to radiation domination before nucleosynthesis; & matter domination subsequently

• Present era: transition to accelerated expansion after structure formation

Impose the constraints:

• tensor-to-scalar ratio spectral index

• Transition to acceleration present value of eq. state parameter

5102 H60N

2102 10250 GeVAGeV

46422 1010 GeVBGeV 44810 GeVC

12.0r 95.0sn

81.0TZ75.00 w

Summary (quintessence & k- essence)[ASM, Phys. Rev. D (2001); N. Bose & ASM, Phys. Rev. D (2009); ibid.]

• We consider quintessence & k-essence models with the interplay of kinetic and potential terms (inspired from unified field theory, higher dimensional models).

• Our aim is to obtain inflation, dark matter & dark energy within a unified framework.

• Predictions of and to be tested with upcoming probes.

• Constraints on model parameters from phenomenological considerations (typically, tuning of potential parameters) Naturalness ? Multiplicity of models.

TZ0w

Backreaction from inhomogeneities (motivation)

Einstein’s equations: nonlinear

Einstein tensor constructed from average metric tensor will not be same in general as the average of the Einstein tensor of the true metric

TG

Acceleration without additional phyics ? Backreaction from inhomogeneities (perspective)[N. Bose & ASM, MNRAS Letters (2011); arXiv:1203.0125]

• Observations tell us that the Universe is inhomogeneous (< 100 Mpc)

• Backreaction from inhomogeneities could modify the evolution of the Universe. Averaging over inhomogeneities to obtain global metric

• Averaging procedure depends on chosen type of hypersurface: constant time or light cone ?

• Backreaction could lead to an accelerated expansion during the present epoch ?

The Backreaction Framework: Einstein equations:

4 3 a

Ga

DDD

D

Q 2 1 1

3 8 2 2

H G D DD DR Q

0 3 t H DD D

where the average of the scalar quantities on the global domain D is

Global domain D is separated into sub-domains

Backreaction

backreaction in subdomain volume fraction of subdomain

1 2 3( , , , )( )

g

g

f t X X X df t

d

D

D

D

23 m m

mH H

DQ Q

Q

Two-scale (interaction-free) void-wall model M – collection of subdomains with initial overdensity (called

“Wall”)

E –– collection of subdomains with initial underdensity (called “Void”)

(power law evolution in subdomains: acceleration equation

Effect of event horizon (Event horizon forms at the onset of acceleration)

Demarcates causally connected regions

;a c t a c t E E M M

3 3 3 3

3 2 3 2

3 3 3 3 2

3 3

( 1) ( 1)1

2 1

h h

h h

h h

h h

c t c ta

a r t r t

c t c t

r r t t

M MD

D

M M

t D

h ta

tdr

)'(

'

Future deceleration due to cosmic backreaction in presence of the event horizon [N. Bose, ASM; MNRAS 2011]

7.00 q(i) α = 0.995, β = 0.5 , (ii) α = 0.999, β = 0.6 ,(iii) α = 1.0, β = 0.5 , (iv) α = 1.02, β = 0.66 .

Parameter space for future deceleration [N. Bose & ASM; arXiv:1203.0125]

Backreaction in presence of event horizon (Summary)

[N. Bose and ASM, MNRAS Letters (2011); arXiv:1203.0125]

• Effect of backreaction due to inhomogeneities on the evolution of the universe • The cosmic event horizon impacts the role of inhomogeneities on the evolution, causing the acceleration to slow down significantly with time.

• Backreaction could be responsible for a decelerated era in the future.(Avoidance of big rip !) more realistic models required. • What is the origin for the onset of acceleration ? No clear answer provided by the backreaction framework

Quantum entanglement and dark energy

Does quantum mechanics (entanglement) play any role in thedynamics of the large-scale universe ?

Two approaches:

• (i) decoherence of quantum wave function (dynamical state vector reduction models) [ASM, D. Home & S. Sinha, Phys. Lett. B (2009)]

• (ii) holographic dark energy from trapped domains (strange quark nuggets) [ASM, S. Sinha, …., under preparation]

Quantum entanglement & Dark Energy (status)

• Two approaches: breaking of quantum entanglement results in dynamical dark energy.

• i) Spontaneous localization of matter wave function (energy exchange with fluctuating scalar field) : using the standard model parameters, DE emerges if the process starts at EW era. [ASM, D. Home, S. Sinha, PLB (2009)]

(comparison with other decoherence models)

• Ii) Holographic dark energy due to trapped baryons in strange quark nuggets (associated with QCD phase transitions). [ASM, S. Sinha, …, under preparation]

Required amount of DE leads to constraints on model parameters (DM—DE scenario).

Summary (Dark energy from various approaches)

• Dark energy : various observations; theoretical puzzle

• Several scenarios – different perspectives

• Category I: no modification of gravitational model; no extra particle physics, e.g., back reaction from observed inhomogeneities – curious feature – present acceleration may be transient (event horizon)

• Category II: Inputs from quantum physics – quantum entanglement and its breaking, e.g., decoherence : (a) spontaneous localization models (b) holographic effects due to trapped domains

• Category III: Scalar field dynamics inspired by unification scenarios

predictions for w, z_T, etc. to be tested by upcoming probes

Some references• Dark energy (unification scenarios)• ASM, Phys. Rev. D 55, 6092 (1997); ASM, Phys. Rev. D 64, 083503 (2001)• N. Bose & ASM, Phys. Rev. D 79, 103517 (2009); Phys. Rev. D 80, 103508 (2009)

• Dark energy (quantum entanglement)• ASM, D. Home, S. Sinha, Phys. Lett. B 679, 167 (2009)

• Dark energy (backreaction from inhomogeneities)• N. Bose & ASM, Mon. Not. R. Astron. Soc. Letters 418, L45 (2011); arXiv:1203.0125-----------------------------------------------------------------------------------------------------------------